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If you drive 0.6 miles along the road and your altitude increases by 150 feet, what is the angle of inclination of the road?
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Give your answer to two decimal places.
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Note that one mile is equal to 5280 feet.
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It can be really useful to sketch a diagram in these sorts of scenarios.
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It will allow you to identify the type of question it is and what you will need to use to be able to solve it.
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Here we have a right-angled triangle, with the hypotenuse representing the slope of the road and the adjacent to the angle representing the horizontal.
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Currently, we have a measurement for the slope as 0.6 miles and a height of 150 feet.
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Before we can go any further, we must ensure all measurements have the same units.
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Weβre given that one mile is equal to 5280 feet.
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We can therefore multiply 0.6 by 5280 to convert 0.6 miles into 3168 feet.
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Now we have a right-angled triangle with two sides given, for which we need to find an angle.
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In that case, we need to use right angle trigonometry to find the missing angle.
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For π, which represents the angle of the inclination of the road, we currently know the length of both the hypotenuse and the opposite.
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In this case, we therefore need to use the sine ratio.
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Substituting what we know into our formula for sin π gives sin π is equal to 150 divided by 3168.
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To calculate the value of π, we work out inverse sin of 180 divided by 3168, which is 2.713.
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The angle of inclination of the road is 2.71 degrees correct to two decimal places.